THE SIZE OP THE EARTH. 15 



Burements of degrees, as follows : The semi-axis major of a 

 rotating spheroid, a form that approximates most closely to 



in the Encyclopaedia Metropolitan a. Ed. of 1849, pp. 220 239. (Here 

 the semi-polar axis was given at 20.853,810 feet=3949.585 miles, the 

 semi-equatorial axis at 20,923,713 feet=3962.824 miles, the meridian 

 quadrant at 32,811,980 feet, and the ellipticity at ^g^ra)- The great 

 astronomer of Konigsberg was uninterruptedly engaged, from 1836 to 

 1842, in calculations regarding the figure of the earth, and as his earlier 

 works were emended by subsequent corrections, the admixture of re- 

 sults of investigations at different periods of time has, in many works, 

 proved a source of great confusion. In numbers, which from their very 

 nature are dependent on one another, this admixture is rendered still 

 more confusing from the erroneous reduction of measurements ; as, for 

 instance, toises, metres, English feet, and miles of 60 and 69 to the 

 equatorial degree ; and this is the more to be regretted since many 

 works, which have cost a very large amount of time and labour, are 

 thus rendered of much less value than they otherwise would be. In 

 the summer of 1837, Bessel published two treatises, one of which was 

 devoted to the consideration of the influence of the irregulai-ity of the 

 earth's figure upon geodetic measurements, and their comparison with 

 astronomical determinations, whilst the other gave the axes of the ob- 

 late spheroid, which seemed to correspond most closely to existing 

 measurements of meridian arcs (Schum. Astr. Nachr. bd. xiv, No. 

 329, s. 269, No. 333, s. 345). The results of his calculation were 

 3271953.854 toises for the semi-axis major; 3261072.900 toises for 

 the semi-axis minor ; and for the length of a mean meridian degree, 

 that is to say, for the ninetieth part of the earth's quadrant (vertically 

 to the equator), 57011.453 toises. An error of 68 toises, or 440.8 feet, 

 which was detected by Puissant, in the mode of calculation that 

 had been adopted, in 1808, by a Commission of the National Institute 

 for determining the distance of the parallels of Montjouy, near 

 Barcelona, and Mola in Formentera, led Bessel, in the year 1841, 

 to submit his previous calculations regarding the dimensions of the 

 earth to a new revision. (Schum. Astr. Nachr. Bd. xix, No. 438, 

 s. 97 116). This correction yielded for the length of the earth's 

 quadrant 5131179.81 toises, instead of 5130740 toises, which had 

 been obtained in accordance with the first determination of the metre ; 

 and for the mean length of a meridian degree, 57013.109 toises, 

 which is about 0.611 of a toise more than a meridian degree, at 

 45 lat. The numbers given in the text are the result of Bessel's latest 

 calculations. The length of the meridian quadrant, 5131180 toises, 

 with a mean error of 255.63 toises, is therefore=10000856 metres, which 

 would tnerefore give 40003423 metres, or 21563.92 geographical miles, 

 for the entire circumference of the earth. The difference between the 

 original assumption of the Commission des Poids et Mesures, according to 

 which the metre was the forty-millionth part of the earth's circumfer- 

 ence, amounts for the entire circumference to 3423 metres, or 1756 27 

 which is almost two geographical miles, or more accurately 



